In a large bowl with a hand or a stand mixer, cream butter and powdered sugar until smooth.
Add vanilla and salt, then mix until smooth.
Add flour, 1 cup at a time, mixing between each addition until completely mixed.
If dough is too sticky to roll at this point, chill for 20 minutes.
Otherwise, divide dough in half. Roll each half out to 1/4-inch thick between two pieces of wax paper or parchment paper.
Chill at least 2 hours or overnight. Chilling the dough lets it rest and adds to the overall flavor of the shortbread.
Preheat oven to 350°F. Line 3 cookie sheets with parchment paper or silicone baking mats.
You can cut your shortbread as desired, using cookie cutters for shapes or circles, but I use a ruler and a pizza cutter to cut squares that are approximately 1-inch by 2-inches. Prick each with the tines of a fork for decoration.
These don’t spread, so you don’t need to space them more than an inch or two on the cookie sheets. Bake for about 14-18 minutes (depending on size of cookie and thickness) until they start to get golden around the edges.
Store in an airtight container for up to 3 days or freeze for up to a month.